Local Discontinuous Galerkin Methods for Solving Convection-Diffusion and Cahn-Hilliard Equations on Surfaces
Numerical Analysis
2024-01-05 v1 Numerical Analysis
Abstract
Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.
Cite
@article{arxiv.2401.02069,
title = {Local Discontinuous Galerkin Methods for Solving Convection-Diffusion and Cahn-Hilliard Equations on Surfaces},
author = {Shixin Xu and Zhiliang Xu},
journal= {arXiv preprint arXiv:2401.02069},
year = {2024}
}